Modeling Backscatter Properties of Snowfall at Millimeter Wavelengths
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MAY 2007 MATROSOV 1727 Modeling Backscatter Properties of Snowfall at Millimeter Wavelengths SERGEY Y. MATROSOV Cooperative Institute for Research in Environmental Sciences, University of Colorado, and NOAA/Earth System Research Laboratory, Boulder, Colorado (Manuscript received 26 April 2006, in final form 20 July 2006) ABSTRACT Ground-based vertically pointing and airborne/spaceborne nadir-pointing millimeter-wavelength radars are being increasingly used worldwide. Though such radars are primarily designed for cloud remote sensing, they can also be used for precipitation measurements including snowfall estimates. In this study, modeling of snowfall radar properties is performed for the common frequencies of millimeter-wavelength radars such as those used by the U.S. Department of Energy’s Atmospheric Radiation Measurement Program (Ka and W bands) and the CloudSat mission (W band). Realistic snowflake models including aggregates and single dendrite crystals were used. The model input included appropriate mass–size and terminal fall velocity–size relations and snowflake orientation and shape assumptions. It was shown that unlike in the Rayleigh scattering regime, which is often applicable for longer radar wavelengths, the spherical model does not generally satisfactorily describe scattering of larger snowflakes at millimeter wavelengths. This is especially true when, due to aerodynamic forcing, these snowflakes are oriented primarily with their major dimensions in the horizontal plane and the zenith/nadir radar pointing geometry is used. As a result of modeling using the experimental snowflake size distributions, radar reflectivity–liquid equivalent snowfall rates (Ze–S) relations are suggested for “dry” snowfalls that consist of mostly unrimed snowflakes containing negligible amounts of liquid water. Owing to uncertainties in the model assumptions, these relations, which are derived for the common Ka- and W-band radar frequencies, have significant variability in their coefficients that can exceed a factor of 2 or so. Modeling snowfall attenuation suggests that the attenuation effects in “dry” snowfall can be neglected at the Ka band for most practical cases, while at the W band attenuation may need to be accounted for in heavier snowfalls observed at longer ranges. 1. Introduction As for rainfall, snowfall radar estimates are typically obtained with longer wavelength (centimeter) radars Traditional radar methods of measuring precipitation such as those that operate at S band (10–11-cm wave- are based on relations between water equivalent reflec- length, ), C band ( ϳ 5–6 cm), or X band ( ϳ 3 cm). tivity factor (hereafter “reflectivity”), Z , and precipi- e Snowfall rate as inferred from radar measurements is tation rate, R. Even for a simpler case of rainfall, there usually expressed in melted liquid equivalent, S, rather are significant variations in Z –R relations due to vari- e than in solid snow rate. Two different approaches are ability of the drop size distributions. Estimating snow- used to derive Z –S relations. In one approach both Z fall parameters from radar measurements is more chal- e e and S are calculated from theoretical or experimental lenging. Variability in snowflake shapes, densities, and snowflake size distributions (SSD) and they are related fall velocities results in greater uncertainties in Z –R e in a statistical manner (e.g., Sekhon and Srivastava relations for snowfall. Notwithstanding these uncertain- 1970; Matrosov 1992). In the second approach, radar ties, radar gives an opportunity to obtain near-real-time measurements of reflectivity are related to the snowfall estimates of snowfall rate and accumulation, providing rate as observed by nearby snow gauges (e.g., Super information that is not readily available with other re- and Holroyd 1998; Hunter and Holroyd 2002). Rasmus- mote sensors. sen et al. (2003) provides a review of some Ze–S rela- tions suggested for use with longer-wavelength radars. Corresponding author address: Dr. Sergey Matrosov, R/PSD2, For such radars, snowflakes are typically much smaller 325 Broadway, Boulder, CO 80305. than radar wavelength and scattering does not deviate E-mail: [email protected] significantly from the Rayleigh law. DOI: 10.1175/JAS3904.1 © 2007 American Meteorological Society JAS3904 1728 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 64 At millimeter radar wavelengths such as those at Ka 2. Snowflake model band ( ϳ 8 mm) and, especially, W band ( ϳ 3 mm), a. Snowflake shape scattering by typical snowflakes is generally non- Rayleigh. Radars operating at these wavelengths have The Rayleigh scattering conditions at a radar wave- been primarily intended for applications in cloud re- length for a snow particle with a major dimension D mote sensing and they have typically not been used for can be formulated as follows: snowfall measurements. It has been shown, however, x ϭ Dր K 1, ͑1͒ that the use of such radars in pair with centimeter- wavelength radars can potentially improve the accuracy | |ր K ͑ ͒ D ms 1, 2 of snowfall parameter retrievals (Matrosov 1998; Liao et al. 2005; Wang et al. 2005) because the dual wave- where ms is the complex refractive index of snow. The length reflectivity ratio provides independent informa- great majority of derivations of Ze–S relations in snow- tion on characteristic size of snowflakes. Knowing size fall assumed that for snowflakes that satisfy these con- information, one can better infer snowfall rate from ditions the radar backscatter would be the same as that single reflectivity measurements. of a sphere of solid ice having the same mass. While this Currently, a number of vertically pointing millime- assumption precludes modeling polarimetric properties ter-wavelength radars operate on a continuing basis in of backscatter cross sections, it provides a reasonably many locations including those that regularly or some- good approximation of Ze for low-density dry snow at times get snowfalls. Examples of such radars are verti- centimeter wavelengths. The spherical model, however, becomes progressively less suitable as the size param- cally pointing K -band (34.6 GHz) millimeter- a eter x increases beyond the bounds of the Rayleigh wavelength cloud radars (MMCR) operated by the U.S. conditions. Larger nonspherical ice particles exhibit Department of Energy’s Atmospheric Radiation Mea- backscatter dependence on particle orientation (e.g., surement Program (DOE ARM) in Oklahoma and the Matrosov 1993; Aydin and Singh 2004) and generally North Slope of Alaska (NSA). Another MMCR-type greater reflectivities (especially outside the Rayleigh radar has been recently deployed in the Canadian Arc- scattering regime) compared to those of spherical par- tic. The W-band (94 GHz) nadir-looking CloudSat ra- ticles of the same mass (Matrosov et al. 2005a). dar will provide global information on reflectivity pro- The simplest geometrical shape that allows describ- files of hydrometeors (Stephens et al. 2002). Although ing nonspherical hydrometeors is that of spheroid. In the main objective of all these radars is cloud remote their classical observational in situ study, Magono and sensing, their measurements of snowfall can also be Nakamura (1965) used tracing outlines of snowflakes interpreted quantitatively, thus providing valuable in- that revealed a generally spheroidal shape. The oblate formation on snowfall accumulation and the vertical spheroidal model is used widely in the radar community structure of snowfall rate, which can vary significantly to model raindrops and it was also shown to satisfacto- (Mitchell 1988). rily describe and explain depolarization observations of Since for most of the radars mentioned above there snowflakes at Ka band (Matrosov et al. 1996, 2001). are no collocated centimeter-wavelength radars for ap- Note also that, at radar frequencies, the small details in plication of dual-wavelength ratio techniques, Ze–S re- a particle structure usually do not significantly affect lations specifically tailored for millimeter wavelengths the backscatter properties that depend largely on the are needed for quantitative interpretation of snowfall overall shape (Dungey and Bohren 1993), which, in the measurements. This article presents results of modeling case of spheroid, is determined by the spheroid aspect Ze–S relations for the common millimeter-wavelength ratio, r. This is especially true for smaller snowflake size frequencies of 34.6 and 94 GHz based on available in- parameters x ϭ DϪ1 (Schneider and Stephens 1995). formation on snowflake-size distributions and densities. The applicability of the spheroid model for larger snow- The first of the aforementioned approaches for deriving flakes with small values of r (e.g., dendrites that are Ze–S relations is employed here because there are no larger than several millimeters) at W band is not so reliable datasets available that combine collocated mil- obvious. This model, however, satisfactorily explains limeter-wavelength radar and snow gauge measure- experimental 94-GHz aggregate snow reflectivities ments. This modeling is concerned with so called “dry” (Matrosov et al. 2005a). snow, the term usually used for describing snow with Based on the arguments given above, and also due to negligible amounts of liquid water/riming. “Dry” snow- the fact that very large dendrites are not very common, falls usually contribute most significantly to snow accu- the oblate spheroidal model was adopted here for mulation at temperatures less than about Ϫ8°C. snowflake